Hands-on Exercise 2A

Author

Kock Si Min

Published

August 31, 2024

Modified

September 1, 2024

1st Order Spatial Point Pattern Analysis Methods

1.1 Learning Outcomes

Spatial Point Pattern Analysis is the evaluation of the pattern or distribution of a set of points on a surface. The point can be a location of:

  • events such as crime, traffic incident and disease onset or

  • business services (coffee and fast food outlets) or facilities such as childcare and eldercare

In this hands-on exercise, we will use appropriate functions of spatstat to discover the spatial point processes of childcare centres in Singapore.

The specific questions to be addressed are as follows:

  • are the childcare centres in Singapore randomly distributed throughout the country?

  • if the answer is not, then the next question is where are the locations with higher concentrations of childcare centres?

1.2 Data Acquisition

Three datasets are used in this exercise:

  • CHILDCARE, a point feature data providing both location and attribute information of childcare centres. It was downloaded from data.gov.sg and is in geojson format.

  • MP14_SUBZONE_WEB_PL, a polygon feature data providing information of URA 2014 Master Plan Planning Subzone boundary data. It is in ESRI shapefile format. This data set was also downloaded from data.gov.sg.

  • CostalOutline, a polygon feature data showing the national boundary of Singapore. It is provided by SLA and is in ESRI shapefile format.

1.3 Installing and Launching R packages

  • sf for importing, managing, and processing vector-based geospatial data, and

  • spatstat, which has a wide range of useful functions for point pattern analysis. In this hands-on exercise, it will be used to perform 1st- and 2nd-order spatial point patterns analysis and derive kernel density estimation (KDE) layer

  • raster which reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.

  • tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.

  • tidyverse for performing data science tasks such as importing, wrangling and visualising data.

The packages are loaded with the following code chunk:

pacman::p_load(sf,spatstat,raster,tmap,tidyverse)

1.4 Spatial Data Wrangling

1.4.1 Importing the spatial data

We will import the geospatial data using st_read() of sf package:

childcare_sf <- st_read("data/geospatial/child-care-services-geojson.geojson") %>%
  st_transform(crs = 3414)
Reading layer `child-care-services-geojson' from data source 
  `C:\mooseksm\ISSS626-GAA\Hands-on_Ex\Hands-on_Ex02\data\geospatial\child-care-services-geojson.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1545 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6824 ymin: 1.248403 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84

Checking whether the EPSG code has been corrected:

st_crs(childcare_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

When the input geospatial data is in shapefile format, two arguments are used:

  • dsn to define the data path

  • layer to provide the shapefile name

sg_sf <- st_read(dsn = "data/geospatial",
                 layer = "CostalOutline")
Reading layer `CostalOutline' from data source 
  `C:\mooseksm\ISSS626-GAA\Hands-on_Ex\Hands-on_Ex02\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 60 features and 4 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21
mpsz_sf <- st_read(dsn = "data/geospatial",
                   layer = "MP14_SUBZONE_WEB_PL")
Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\mooseksm\ISSS626-GAA\Hands-on_Ex\Hands-on_Ex02\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

Before using these data for analysis, it is important to ensure that they are projected in the same projection system.

st_crs(sg_sf)
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]
st_crs(mpsz_sf)
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]

While the sg_sf and mpsz_sf data frames are projected in svy21, the end of the printout above states that the EPSG is 9001 - this is a wrong EPSG code as the correct EPSG code for svy21 should be 3414.

To correctly assign the right EPSG code to both data frame, st_set_crs() of sf package is used:

sg_sf3414 <- st_set_crs(sg_sf,3414)
mpsz_sf3414 <- st_set_crs(mpsz_sf,3414)

Checking whether the EPSG code has been corrected:

st_crs(sg_sf3414)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
st_crs(mpsz_sf3414)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

1.4.2 Mapping the geospatial datasets

After checking the referencing system of each geospatial dataframe, it is also useful to plot a map to show their spatial patterns. A pin map can be prepared using the code below:

tmap_mode('view')
tm_shape(childcare_sf)+
  tm_dots()

All the geospatial layers are within the same map extend which indicates that their referencing system and coordinate values are referred to similar spatial context. This is very important in any geospatial analysis.

tmap_mode('plot')

At interactive mode, tmap is using leaflet for RAPI. The advantage of an interactive pin map is it allows one to navigate and zoom around the map freely as well as query the information of each simple feature (i.e. the point) by clicking on the. The background of the internet map layer can also be changed. At present, three internet map layers are provided: ESRI.WorldGrayCanvas, OpenStreetMap, and ESRI.WorldTopoMap. The default is ESRI.WorldGrayCanvas.

Tip

It is always important to switch back to plot mode after the interactive map as each interactive mode will consume a connection.

It is important to avoid displaying excessive number of interactive maps i.e. not more than 10, in one RMarkdown document when publishing on Netlify.

1.5 Geospatial Data Wrangling

While simple feature data frame is gaining popularity against Spatial* classes, many geospatial analysis packages require the input geospatial data in to be in Spatial* classes. In this section, simple feature data frame will be converted to Spatial* class.

1.5.1 Converting sf dataframes to sp’s Spatial* class

The code chunk below uses as_Spatial() of sf package to convert the three geospatial data from simple feature data frame to sp’s Spatial* class.

childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf3414)
sg <- as_Spatial(sg_sf3414)
childcare
class       : SpatialPointsDataFrame 
features    : 1545 
extent      : 11203.01, 45404.24, 25667.6, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 2
names       :    Name,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Description 
min values  :   kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>018989</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>1, MARINA BOULEVARD, #B1 - 01, ONE MARINA BOULEVARD, SINGAPORE 018989</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>THE LITTLE SKOOL-HOUSE INTERNATIONAL PTE. LTD.</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>08F73931F4A691F4</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
max values  : kml_999,                  <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>829646</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>200, PONGGOL SEVENTEENTH AVENUE, SINGAPORE 829646</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>RAFFLES KIDZ @ PUNGGOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>379D017BF244B0FA</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
mpsz
class       : SpatialPolygonsDataFrame 
features    : 323 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 15
names       : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C,       REGION_N, REGION_C,          INC_CRC, FMEL_UPD_D,     X_ADDR,     Y_ADDR,    SHAPE_Leng,    SHAPE_Area 
min values  :        1,          1, ADMIRALTY,    AMSZ01,      N, ANG MO KIO,         AM, CENTRAL REGION,       CR, 00F5E30B5C9B7AD8,      16409,  5092.8949,  19579.069, 871.554887798, 39437.9352703 
max values  :      323,         17,    YUNNAN,    YSSZ09,      Y,     YISHUN,         YS,    WEST REGION,       WR, FFCCF172717C2EAF,      16409, 50424.7923, 49552.7904, 68083.9364708,  69748298.792 
sg
class       : SpatialPolygonsDataFrame 
features    : 60 
extent      : 2663.926, 56047.79, 16357.98, 50244.03  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 4
names       : GDO_GID, MSLINK, MAPID,              COSTAL_NAM 
min values  :       1,      1,     0,             ISLAND LINK 
max values  :      60,     67,     0, SINGAPORE - MAIN ISLAND 

The geospatial data have been converted into their respective sp’s Spatial* classes now.

1.5.2 Converting the Spatial* class into generic sp format

spatstat requires the analytical data in ppp object form. There is no direct way to convert a Spatial* classes into ppp object. We need to convert the Spatial classes* into Spatial object first.

The codes chunk below converts the Spatial* classes into generic sp objects.

childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg,"SpatialPolygons")
childcare_sp
class       : SpatialPoints 
features    : 1545 
extent      : 11203.01, 45404.24, 25667.6, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
sg_sp
class       : SpatialPolygons 
features    : 60 
extent      : 2663.926, 56047.79, 16357.98, 50244.03  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

1.5.3 Converting generic sp format into spatstat’s ppp format

Now, we will use as.ppp() function of spatstat to convert the spatial data into spatstat’s ppp object format.

childcare_ppp <- as.ppp(childcare_sf)
childcare_ppp
Marked planar point pattern: 1545 points
marks are of storage type  'character'
window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units

Plotting childcare_ppp:

plot(childcare_ppp)

Taking a look at the summary statistics of the ppp object:

summary(childcare_ppp)
Marked planar point pattern:  1545 points
Average intensity 1.91145e-06 points per square unit

Coordinates are given to 11 decimal places

marks are of type 'character'
Summary:
   Length     Class      Mode 
     1545 character character 

Window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
                    (34200 x 23630 units)
Window area = 808287000 square units
Note

In spatial point patterns analysis, a significant issue is the presence of duplicates. The statistical methodology used for spatial point patterns processes is based largely on the assumption that process is simple, that is, that the points cannot be coincidental.

1.5.4 Handling duplicate points

We can check the duplication in a ppp object using the code chunk below:

any(duplicated(childcare_ppp))
[1] FALSE

To count the number of coincidence points, the multiplicity() function is used, as shown in the code chunk below.

multiplicity(childcare_ppp)
   [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1518] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

To know how many locations have more than one point event, the code chunk below is used:

sum(multiplicity(childcare_ppp) > 1)
[1] 0
tmap_mode('view')
tm_shape(childcare) +
  tm_dots(alpha=0.4, 
          size=0.05)
tmap_mode('plot')

In the event of duplicate points, there are 3 ways to overcome the issue:

  1. Delete the duplicates - easiest way but it will also meant that some useful point events will be lost
  2. Jittering - this method will add a small perturbation to the duplicate points so that they do not occupy the exact same space
  3. Make each point “unique” and attach the duplicates of the points to the patterns as marks, as attributes of the points. Analytical techniques that take into account these marks would be required.

The code chunk below implements the jittering approach:

childcare_ppp_jit <- rjitter(childcare_ppp, 
                             retry=TRUE, 
                             nsim=1, 
                             drop=TRUE)

Check for duplicated points:

any(duplicated(childcare_ppp_jit))
[1] FALSE

1.5.5 Creating owin object

When analysing spatial point patterns, it is a good practice to confine the analysis within a geographical area like Singapore’s boundary. In spatstat, an object called owin is specially designed to represent this polygonal region.

The code chunk below is used to covert sg SpatialPolygon object into owin object of spatstat.

sg_owin <- as.owin(sg_sf)

The ouput object can be displayed by using plot() function:

plot(sg_owin)

summary(sg_owin)
Window: polygonal boundary
50 separate polygons (1 hole)
                 vertices         area relative.area
polygon 1 (hole)       30     -7081.18     -9.76e-06
polygon 2              55     82537.90      1.14e-04
polygon 3              90    415092.00      5.72e-04
polygon 4              49     16698.60      2.30e-05
polygon 5              38     24249.20      3.34e-05
polygon 6             976  23344700.00      3.22e-02
polygon 7             721   1927950.00      2.66e-03
polygon 8            1992   9992170.00      1.38e-02
polygon 9             330   1118960.00      1.54e-03
polygon 10            175    925904.00      1.28e-03
polygon 11            115    928394.00      1.28e-03
polygon 12             24      6352.39      8.76e-06
polygon 13            190    202489.00      2.79e-04
polygon 14             37     10170.50      1.40e-05
polygon 15             25     16622.70      2.29e-05
polygon 16             10      2145.07      2.96e-06
polygon 17             66     16184.10      2.23e-05
polygon 18           5195 636837000.00      8.78e-01
polygon 19             76    312332.00      4.31e-04
polygon 20            627  31891300.00      4.40e-02
polygon 21             20     32842.00      4.53e-05
polygon 22             42     55831.70      7.70e-05
polygon 23             67   1313540.00      1.81e-03
polygon 24            734   4690930.00      6.47e-03
polygon 25             16      3194.60      4.40e-06
polygon 26             15      4872.96      6.72e-06
polygon 27             15      4464.20      6.15e-06
polygon 28             14      5466.74      7.54e-06
polygon 29             37      5261.94      7.25e-06
polygon 30            111    662927.00      9.14e-04
polygon 31             69     56313.40      7.76e-05
polygon 32            143    145139.00      2.00e-04
polygon 33            397   2488210.00      3.43e-03
polygon 34             90    115991.00      1.60e-04
polygon 35             98     62682.90      8.64e-05
polygon 36            165    338736.00      4.67e-04
polygon 37            130     94046.50      1.30e-04
polygon 38             93    430642.00      5.94e-04
polygon 39             16      2010.46      2.77e-06
polygon 40            415   3253840.00      4.49e-03
polygon 41             30     10838.20      1.49e-05
polygon 42             53     34400.30      4.74e-05
polygon 43             26      8347.58      1.15e-05
polygon 44             74     58223.40      8.03e-05
polygon 45            327   2169210.00      2.99e-03
polygon 46            177    467446.00      6.44e-04
polygon 47             46    699702.00      9.65e-04
polygon 48              6     16841.00      2.32e-05
polygon 49             13     70087.30      9.66e-05
polygon 50              4      9459.63      1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
                     (53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.401

1.5.6 Combining point events object and owin object

In this last step of geospatial data wrangling, we will extract childcare events that are located within Singapore by using the code chunk below:

childcareSG_ppp = childcare_ppp[sg_owin]

The output object combined both the point and polygon feature in one ppp object class as shown below:

summary(childcareSG_ppp)
Marked planar point pattern:  1545 points
Average intensity 2.129929e-06 points per square unit

Coordinates are given to 11 decimal places

marks are of type 'character'
Summary:
   Length     Class      Mode 
     1545 character character 

Window: polygonal boundary
50 separate polygons (1 hole)
                 vertices         area relative.area
polygon 1 (hole)       30     -7081.18     -9.76e-06
polygon 2              55     82537.90      1.14e-04
polygon 3              90    415092.00      5.72e-04
polygon 4              49     16698.60      2.30e-05
polygon 5              38     24249.20      3.34e-05
polygon 6             976  23344700.00      3.22e-02
polygon 7             721   1927950.00      2.66e-03
polygon 8            1992   9992170.00      1.38e-02
polygon 9             330   1118960.00      1.54e-03
polygon 10            175    925904.00      1.28e-03
polygon 11            115    928394.00      1.28e-03
polygon 12             24      6352.39      8.76e-06
polygon 13            190    202489.00      2.79e-04
polygon 14             37     10170.50      1.40e-05
polygon 15             25     16622.70      2.29e-05
polygon 16             10      2145.07      2.96e-06
polygon 17             66     16184.10      2.23e-05
polygon 18           5195 636837000.00      8.78e-01
polygon 19             76    312332.00      4.31e-04
polygon 20            627  31891300.00      4.40e-02
polygon 21             20     32842.00      4.53e-05
polygon 22             42     55831.70      7.70e-05
polygon 23             67   1313540.00      1.81e-03
polygon 24            734   4690930.00      6.47e-03
polygon 25             16      3194.60      4.40e-06
polygon 26             15      4872.96      6.72e-06
polygon 27             15      4464.20      6.15e-06
polygon 28             14      5466.74      7.54e-06
polygon 29             37      5261.94      7.25e-06
polygon 30            111    662927.00      9.14e-04
polygon 31             69     56313.40      7.76e-05
polygon 32            143    145139.00      2.00e-04
polygon 33            397   2488210.00      3.43e-03
polygon 34             90    115991.00      1.60e-04
polygon 35             98     62682.90      8.64e-05
polygon 36            165    338736.00      4.67e-04
polygon 37            130     94046.50      1.30e-04
polygon 38             93    430642.00      5.94e-04
polygon 39             16      2010.46      2.77e-06
polygon 40            415   3253840.00      4.49e-03
polygon 41             30     10838.20      1.49e-05
polygon 42             53     34400.30      4.74e-05
polygon 43             26      8347.58      1.15e-05
polygon 44             74     58223.40      8.03e-05
polygon 45            327   2169210.00      2.99e-03
polygon 46            177    467446.00      6.44e-04
polygon 47             46    699702.00      9.65e-04
polygon 48              6     16841.00      2.32e-05
polygon 49             13     70087.30      9.66e-05
polygon 50              4      9459.63      1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
                     (53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.401

Plotting the newly derived childcareSG_ppp:

plot(childcareSG_ppp)

1.6 First-order Spatial Point Patterns Analysis

In this section, first-order SPPA will be performed using spatstat package. The hands-on exercise will focus on:

  • deriving kernel density estimation (KDE) layer for visualising and exploring the intensity of point processes,

  • performing Confirmatory Spatial Point Patterns Analysis by using Nearest Neighbour statistics.

1.6.1 Kernel Density Estimation

In this section, we will compute the kernel density estimation (KDE) of childcare services in Singapore.

1.6.1.1 Computing kernel density estimation using automatic bandwidth selection method

The code chunk below computes a kernel density by using the following configurations of density() of spatstat:

  • bw.diggle() automatic bandwidth selection method. Other recommended methods are bw.CvL(), bw.scott() or bw.ppl().

  • The smoothing kernel used is gaussian, which is the default. Other smoothing methods are: “epanechnikov”, “quartic” or “disc”.

  • The intensity estimate is corrected for edge effect bias by using method described by Jones (1993) and Diggle (2010, equation 18.9). The default is FALSE.

kde_childcareSG_bw <- density(childcareSG_ppp,
                              sigma=bw.diggle,
                              edge=TRUE,
                            kernel="gaussian") 

The plot() function of Base R is then used to display the kernel density derived.

plot(kde_childcareSG_bw)

The density values of the output range from 0 to 0.000035 which is way too small to comprehend. This is because the default unit of measurement of svy21 is in meter. As a result, the density values computed is in “number of points per square meter”.

As added info, the bandwidth used to compute the kde layer can be retrieved using the code chunk below:

bw <- bw.diggle(childcareSG_ppp)
bw
   sigma 
298.4095 

1.6.1.2 Re-scaling KDE values

In the code chunk below, rescale.ppp() is used to covert the unit of measurement from meter to kilometer:

childcareSG_ppp.km <- rescale.ppp(childcareSG_ppp, 1000, "km")

Re-run density() using the resale data set and plot the output kde map:

kde_childcareSG.bw <- density(childcareSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG.bw)

Note that the output image looks identical to the earlier version and that the only change is in the data values (refer to the legend).

1.6.2 Working with different automatic badwidth methods

Beside bw.diggle(), there are three other spatstat functions can be used to determine the bandwidth, they are: bw.CvL(), bw.scott(), and bw.ppl().

 bw.CvL(childcareSG_ppp.km)
   sigma 
4.543278 
bw.scott(childcareSG_ppp.km)
 sigma.x  sigma.y 
2.224898 1.450966 
bw.ppl(childcareSG_ppp.km)
    sigma 
0.3897114 
bw.diggle(childcareSG_ppp.km)
    sigma 
0.2984095 

Baddeley et. (2016) suggested the use of the bw.ppl() algorithm as from their experience, this method tends to produce more appropriate values when the pattern consisted predominantly of tight clusters. However, if the purpose of thestudy is to detect a single tight cluster in the midst of random noise, the bw.diggle() method seemed to work best.

The code chunk beow will be used to compare the output of using bw.diggle and bw.ppl methods:

kde_childcareSG.ppl <- density(childcareSG_ppp.km, 
                               sigma=bw.ppl, 
                               edge=TRUE,
                               kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")

1.6.3 Working with different kernel methods

By default, the kernel method used in density.ppp() is gaussian. But there are three other options, namely: Epanechnikov, Quartic and Dics.

The code chunk below will be used to compute three more kernel density estimations by using these three kernel function:

par(mfrow=c(2,2))
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="gaussian"), 
     main="Gaussian")
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="epanechnikov"), 
     main="Epanechnikov")
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="quartic"), 
     main="Quartic")
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="disc"), 
     main="Disc")

1.7 Fixed and Adaptive KDE

1.7.1 Computing KDE by using fixed bandwidth

Next, a KDE layer will be computed by defining a bandwidth of 600 meter. In the code chunk below, the sigma value used is 0.6. as the unit of measurement of childcareSG_ppp.km object is in kilometer, hence the 600m is 0.6km.

kde_childcareSG_600 <- density(childcareSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG_600)

1.7.2 Computing KDE by using adaptive bandwidth

Fixed bandwidth method is very sensitive to highly skew distribution of spatial point patterns over geographical units for example urban versus rural. One way to overcome this problem is by using adaptive bandwidth instead.

In this section, adaptive kernel density estimation will be derived using density.adaptive() of spatstat.

kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)

We can compare the fixed and adaptive kernel density estimation outputs by using the code chunk below.

par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")

1.7.3 Converting KDE output into grid object

We convert the result to be suitable for mapping purposes:

gridded_kde_childcareSG_bw <- as.im(kde_childcareSG.bw)
plot(gridded_kde_childcareSG_bw)

1.7.3.1 Converting gridded output into raster

Next, the gridded kernal density objects will be converted into a RasterLayer object by using raster() of raster package:

kde_childcareSG_bw_raster <- raster(kde_childcareSG.bw)

Taking a look at the properties of kde_childcareSG_bw_raster RasterLayer:

kde_childcareSG_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348  (x, y)
extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
crs        : NA 
source     : memory
names      : layer 
values     : -8.476185e-15, 28.51831  (min, max)

Note that the crs property is NA.

1.7.3.2 Assigning projection systems

The code chunk below will be used to include the CRS information on kde_childcareSG_bw_raster RasterLayer:

projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348  (x, y)
extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
crs        : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs 
source     : memory
names      : layer 
values     : -8.476185e-15, 28.51831  (min, max)

The crs property is now completed.

1.7.4 Visualising the output in tmap

Finally, we will display the raster in cartographic quality map using tmap package:

tm_shape(kde_childcareSG_bw_raster) + 
  tm_raster("layer", palette = "viridis") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

Note that the raster values are encoded explicitly onto the raster pixel using the values in “v”” field.

1.7.5 Comparing Spatial Point Patterns using KDE

In this section, the KDE of childcare at Ponggol, Tampines, Chua Chu Kang and Jurong West planning areas will be compared.

1.7.5.1 Extracting study area

The code chunk below will be used to extract the target planning areas.

pg <- mpsz_sf %>%
  filter(PLN_AREA_N == "PUNGGOL")
tm <- mpsz_sf %>%
  filter(PLN_AREA_N == "TAMPINES")
ck <- mpsz_sf %>%
  filter(PLN_AREA_N == "CHOA CHU KANG")
jw <- mpsz_sf %>%
  filter(PLN_AREA_N == "JURONG WEST")

Plotting target planning areas:

par(mfrow=c(2,2))
plot(pg, main = "Punggol")

plot(tm, main = "Tampines")

plot(ck, main = "Choa Chu Kang")

plot(jw, main = "Jurong West")

1.7.5.2 Creating owin object

Now, we will convert these sf objects into owin objects that is required by spatstat:

pg_owin = as.owin(pg)
tm_owin = as.owin(tm)
ck_owin = as.owin(ck)
jw_owin = as.owin(jw)

1.7.5.3 Combining childcare points and the study area

By using the code chunk below, we are able to extract childcare that is within the specific region to do our analysis later on.

childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]

Next, rescale.ppp() function is used to transform the unit of measurement from metre to kilometre:

childcare_pg_ppp.km = rescale.ppp(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale.ppp(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale.ppp(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale.ppp(childcare_jw_ppp, 1000, "km")

The code chunk below is used to plot these four study areas and the locations of the childcare centres:

par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")

1.7.5.4 Computing KDE

The code chunk below will be used to compute the KDE of these four planning area. bw.diggle method is used to derive the bandwidth of each area:

par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Punggol")
plot(density(childcare_tm_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tampines")
plot(density(childcare_ck_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Jurong West")

1.7.5.5 Computing fixed bandwidth KDE

For comparison purposes, 250m will be used as the bandwidth:

par(mfrow=c(2,2))
plot(density(childcare_ck_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Chou Chu Kang")
plot(density(childcare_jw_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Jurong West")
plot(density(childcare_pg_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Punggol")
plot(density(childcare_tm_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tampines")

1.8 Nearest Neighbour Analysis

In this section, we will perform the Clark-Evans test of aggregation for a spatial point pattern by using clarkevans.test() of statspat.

The test hypotheses are:

H0 = The distribution of childcare services are randomly distributed.

H1= The distribution of childcare services are not randomly distributed.

The 95% confidence interval will be used.

1.8.1 Testing spatial point patterns using Clark and Evans Test

clarkevans.test(childcareSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcareSG_ppp
R = 0.55631, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)

1.8.2 Clark and Evans Test: Choa Chu Kang planning area

In the code chunk below, clarkevans.test() of spatstat is used to performs Clark-Evans test of aggregation for childcare centre in Choa Chu Kang planning area:

clarkevans.test(childcare_ck_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_ck_ppp
R = 0.94527, p-value = 0.4135
alternative hypothesis: two-sided

1.8.3 Clark and Evans Test: Tampines planning area

In the code chunk below, the similar test is used to analyse the spatial point patterns of childcare centre in Tampines planning area:

clarkevans.test(childcare_tm_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_tm_ppp
R = 0.79076, p-value = 0.0001592
alternative hypothesis: two-sided